5 Answers
5

Got is acceptable in informal discourse, but became is to be preferred in formal discourse.

This is not entirely a matter of register, however. Get always has a certain overtone of acquire, and suggesting that ubiquity is a quality acquired by computers is a little wonky. You'd be more likely to say that computers got faster or got more powerful than got more ubiquitous.

A side issue is whether ubiquitous is in fact scalable; I don't particularly object to more ubiquitous, since it’s understood as what I would phrase as more nearly ubiquitous, but some have a legitimate argument against it. You might avoid the quarrel by writing “As computing came to play a greater and greater role in people’s daily lives ...”

thank you for this detailed comment .. after re-thinking the sentence I want to write again I followed your suggestion regarding the scalability of "ubiquitous". I've added my conclusion the my original post. Thank you!
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marc wellmanDec 27 '12 at 16:01

"As computing became more and more ubiquitous..." is preferable, but ubiquity is better understood as an absolute condition: something is either ubiquitous or it isn't.
How about: "As the use of computers became increasingly common in daily life..."

Get is one of those verbs that has many forms and could work in a context like yours the same way become does. It seems to be marked informal in formal discourse. So if it's a written and more formal document, become will be a better choice and will keep you on the safe side.